William M. Briggs

Statistician to the Stars!

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Has atmospheric CO2 decreased? A different way to look at CO2 changes

Joe Daleo, the number one guy over at Icecap.us, recently sent me the CDIAC (ice core) CO2 data as criticized in Beck (2007) and asked me what I made of it. Now, this data has been pored over by the great and small, so should we expect any revelations along the lines of “Has CO2 actually decreased?” Well…see below. I don’t often see this data pictured in one particular way that I find instructive, so I wanted to show it to you.

You’re probably used to seeing CO2 through time in plots very much like this cartoon.

CO2 through time

The black line is the actual CO2 data, the two background colors representing, before 1958, estimates of CO2 based on ice cores, and after that on measurements from Mauna Loa. The green line is a suitably normalized estimate of the human population. Both increase at what looks like roughly the same rate. Right?

Side note: these are estimates, and, ideally, both lines would have a “plus or minus” line plotted above and below so that we can see the graphical representation of the uncertainty in the numbers, which might, or might not be, substantial. I don’t know what the error is for either curve, but we’ll ignore this not inconsequential problem today.

Now let’s take the exact same data and plot it in a slightly different way.

Log CO2 change through time

Click the image for larger version: you may wish to right click and “Open Link In New Window” (or words like that) so that you can view the graph and read its description at the same time. Or download a printable pdf version here.

This graph is complicated, so let’s take our time to understand it. The horizontal, or bottom, axis is still time. But now the black line is the yearly change in CO2. For example, in 2007 the CO2 was measured to be 383.32 parts per million (ppm) and for 2006 it was 381.83 ppm. The change, which was an increase, was 1.49 ppm. We measure this change for each year and keep the results, so that we can see the rate of increase (or possible decrease or no change) for each year. We could plot this raw change through time, but a lot of detail is hidden because the increase is exponential (the same shape as the cartoon plot above).

Instead of a raw plot, we take the log of all values so that detail can emerge. This should not change conclusions based on the data in any way, and it does allow us to see it better (technical note: the value of 1.2 was added to all values because some changes were negative and, without using complex numbers, we cannot take logarithms of negative numbers).

The detail pops now, doesn’t it? The first thing to notice is the marked qualitative and quantitative differences in the Mauna Loa and Ice Core estimates. The two methods are obviously not directly compatible, a fact which was hidden in the raw (non-differenced) plots. This makes decisions about the rate of increase of CO2 across the two regimes trickier than is commonly thought.

First concentrate just on the Mauna Loa regime. The rate of change has been over-plotted by a simple regression line, which fits rather well (I’ll spare you the formal statistical tests: but trust me). That is, the model of exponential acceleration of CO2 into the atmosphere is well supported over this range. This is acceleration because, recall, that this plot of the rate of increase of CO2.

To explain that further: suppose, every year, the exact same amount of new CO2 is added to the atmosphere. The graph for that would then be a straight line on our plot, which is roughly the case for the dates 1750 to 1800. During that time, about 0.12 ppm of new CO2 was added each year. At least, according to the estimates from ice cores.

To emphasize: if our graph shows a (rough) increasing line, as it does in the Mauna Loa regime, then the rate at which CO2 is being added to the atmosphere (according the chemical measurement method used) is increasing. If the graph shows a straight line for certain periods, then those periods contributed the same amount of new CO2 each year. But if the graph shows a (rough) decreasing line, as it does in several place in the ice core regime, then the amount of new CO2 being added to the atmosphere is decelerating: new CO2 is still being added, but at a slower rate.

There are even times when CO2 has decreased, i.e. removed from the atmosphere, from year to year (according to the measurements used): these are the points below the dotted-dashed line at 0. These times were roughly 1820, 1831-1838, times before wide-scale industrialization, and 1942-1944. 1942 to 1944? This was certainly a time in which the entire world, if you recall, was intent on adding as much of everything to the atmosphere that it possibly could. So this result is strange. One possibility is measurement error: something might have gone wrong in the way the ice cores were processed.

It is usually thought that the measurement method used for ice cores is accurate and unbiased and so on. So suppose that is true. Then it cannot have been the war that accounts for this dip in the mid-1940s, because there is no similar dip around the years of The Great War. In fact, during that time, the rate of new CO2 was accelerating, as indicated by the regression fit over the years 1898 to 1941.

Just for fun, I have drawn the two regression lines, for the ice core and Mauna Loa regimes, extending forwards and backwards through time (these are the light dotted lines). What I learn from this, again, is that the two measurement methods are probably not compatible.

On to the human population, again pictured in green, but here, like CO2, we are looking at logged differences in year to year population, suitably normalized for ease of comparison. Data from 1950 to 2007 was available for each year from the U.S. Census Bureau; from before that, I used, Lord help me, Wikipedia. Estimates before 1950 were sparse, generally only available every 50 years or so. I fit a variety of splines (B-splines, polynomial, etc.) and even a strict linear interpolation to estimate the missing values: all methods gave substantially the same results. What we have to say about human population isn’t that crucial, anyway.

You first see two dips, one around 1915 or so and another from the late 1940s. These dips certainly are from the two World Wars. Population was still increasing then, but, obviously, at a slower rate. The deceleration from the late 1960s to present time is well known to demographers: while population is still increasing, the rate at which it is doing so is dramatically decreasing, particularly in Enlightened countries. The odd dip around 1960 is probably due to the utopian joys of communism: Mao’s great leap forward (into the grave, apparently).

Ok, that’s the data. But it only takes us so far: human population numbers are only a rough, very rough, proxy of our ability to add CO2 to the air. For example, during 1831-1838 the human population was accelerating but the CO2 was decelerating! Human population also dropped during World War II, the same time as a measured drop of atmospheric CO2, as mentioned above. But a similar deceleration in human population in World War I did not find a concomitant deceleration of CO2.

What to make of plots of people versus CO2? My guess: not much. Particularly since current rates of population are decelerating and will continue to do so, yet CO2 rates are accelerating. The correlation between human population and CO2 is just too noisy and inexact to be of much use.

I am not an expert in measuring atmospheric CO2, but I will make three conclusions which I believe are well supported statistically. (1) The two methods of measuring CO2: ice core reconstruction and air-chemical, are not compatible. One is over-estimating or one is under-estimating. I have no idea which is which; whether, that is, historical numbers should be adjusted higher or current numbers should be estimated lower. Beck (2007) and Jaworski (2007) argue that the historical numbers are low.

(2) We should increase our uncertainty in models, such as global climate models, that use this CO2 data as input, particularly if they use the data which spans the two measurement regimes.

(3) There are odd discrepancies, unexplainable through human population correlations, in the ice core data. At times CO2 has been measured to actually decrease. This might be true, but the times of the decreases are not consonant with human activities. Clearly, measurement error is a likely possibility and should be investigated.

Lastly, of course, there is Beck’s paper, which is essential reading on this subject. I do not have Beck’s data, just the ice core data: some of the same signals, though not the same in magnitude, in the CDIAC data are also in Beck. His contention, supported by data, is that CO2 has been higher in the recent past. Like a peak around 1940 or so, declining afterwards: the decrease we also see.

I might be wrong about all this, so I welcome comments and discussion.

Beck, E.G., 2007. 180 years of atmospheric CO2 gas analysis by chemical methods. Energy and Environment, 18, No. 2, 259-282.
Jaworowski, Z., 2007. CO2: the greatest scientific scandal of our time. EIR: Science, 16 March, 38-53.

Mandatory suicide to reduce carbon footprint no joke

In an interview with Stephen Wright at Cracked.com, the comedian tells a favorite joke: You never know what you have until it’s gone, and I wanted to know what I had, so I got rid of everything. He lamented, “I really like that one, but it didn’t really get a laugh.”

Every comedian has a story of a beloved joke that never gets a laugh, and of other quips that everybody inexplicably likes.

I tell you this my friends because I worry about you. My number two son and I posted a “story” about Zombie Attacks Increasing Due to Global Warming, and the thing is linked at hundreds, and at a growing number, of websites. But the next day’s post—in my opinion, my most hilarious—about people willfully turning themselves into Soylent Green to battle climate change didn’t even rate a chuckle. Many of you even took it seriously! You can’t go wrong with Zombies, I guess. (By the way, check out waywardrobot.com today.)

The posting on the Soylent Coroporation’s government contract to encourage people to Go Home–i.e., commit suicide—to reduce their “carbon footprint” was, of course, a satirical observation on the zany lengths to which people will go when swayed by ideology. But it actually wasn’t too far off the mark.

How do I know this? Well, according to this fine article by Brad Allenby at GreenBiz.com, a “recent study from the Swedish Ministry of Sustainable Development argues that males have a disproportionately larger impact on global warming” because “women cause considerably fewer carbon dioxide emissions than men and thus considerably less climate change.” So we need fewer men.

Think the worst of sins is driving an SUV? Not a chance. Being obese and having children also up people’s carbon output. Eating meat is bad, too. These behaviors obviously have to be curtailed, if not voluntarily, then at some point by force—force of law, of course.

It might not come to that. There might be enough deeply concerned volunteers to pull the load for the rest of us. Says humble citizen Erik Daehler, in an article about how we can all do out part, “You do have to sacrifice,” said Daehler. “I think a lot of people are going to have to soon assess themselves and figure out that what they give up now may allow their kids to have it, or their kids’ kids to have it. It’s sort of a selfish relationship we have with the environment right now.”

But even reducing your [carbon] footprint to zero and living a so-called carbon neutral life may not be enough, said the [director of the Natural Resources Defense Council's climate change program John] Steelman.

You can take yourself out of the equation,” he said…(emphasis mine)

[Ordinary citizen] Tony Napolillo said he won’t wait for politicians to act.

“Everybody has to realize they have personal responsibility,” he said. “They can’t just wait for the government or the corporate world to do something about it. If everybody could strive to be carbon neutral, this would be a greater world.”

It’s never too long these days before reality overtakes parody, so I should take my own advice and leave well enough alone, before somebody does think “Going Home” is a good idea.

San Francisco mandatory carbon-footprint reduction program begins

Mayor Gavin Newsom announced that San Francisco’s mandatory carbon-footprint reduction program will begin as scheduled on the first of March.

“There never was a problem as serious as global warming and we must take action now,” said mayoral spokesman William Simonson. “San Franciscans are among the most enlightened people of the world and they are eager to do their part,” he continued.

Phase One of the program requires all citizens to cease jogging and other aerobic activities. “Each time a San Franciscan exhales, they add to the already over-burdened carbon dioxide load of the atmosphere.” Simonson explained that “jogging increases the amount of CO2 in people’s breath to unacceptable levels.” All jogging paths will be converted to green space which will also help absorb CO2. Conversion is expected to last at least three years.

The more controversial part of the program is Phase Two, which is expected to remain voluntary. “Each citizen must decide whether Phase Two”—which the mayor has dubbed Going Home—”is right for them.” A public square highlighting a monument on which will be engraved a listing of the volunteers will be opened downtown by late summer. All work on the square has been donated by Gore Enterprises.

“We hope that this beautiful place will encourage more people, not just here in San Francisco, but all over the world to do their part,” said the mayor.

Phase Two is not without controversy. Bob Thorn of Let Us Breath, a non-profit group, said, “This program will never remain purely voluntary. This is just the mayor playing politics.”

Simonson has been quoted as saying that there are no plans to make Phase Two mandatory. “We will visit that issue if our carbon sequestration goals have not been met.” He added that the Let Us Breath’s “scare tactics” were typical of “climate denialists” and that everybody so far has expressed “nothing but support” for the program.

Gore enterprises is a subsidiary of the Soylent Corporation, makers of Soylent Green®.

Zombies no joke: global warming can cause anything

A day ago my number two son and I sat over a bottle of wine and he suggested that if global warming caused temperatures to increase, then we would see an escalation in the number of zombie attacks because, obviously, there would be less cold weather, which everybody knows slows attacks from the undead. I wrote this up in the approved New York Times format, and, to my astonishment, some people thought I was joking.

I was not. The post was in earnest and was an attempt to put into perspective the hundreds, if not thousands, of “studies” that purport to show the ills that will befall us when global warming finally strikes. There are three problems with these studies.

The first is their ridiculous variety, nowhere better cataloged than at NumberWatch’sWarm List“. That page contains links, mostly to news reports to studies that ask us to believe that, for example, lizards will undergo sex changes, there will be “waves of rape“, a rash of camel deaths will occur, the Earth will spin faster (hold on!), and, worst and most frightening of all, there will be an increase in lawyers (to handle all the “who’s fault is it?” litigation, you see).

I listed only five of the hundreds on that page, which no doubt represents an undercount of the true number of worrying research reports. New ones appear daily. If you wanted to adopt a cynical attitude, you might think there is an unstated competition among researchers to see who can get the most of these or the most shocking of these things to press.

Can these studies all be true? Yes, it logically is possible, only it is absurd to think so. The probability of each and every one of these calamities coming to pass is as close to zero as you like. But that’s not the real problem. It is that each of these studies is usually taken as further proof, albeit indirect, that significant man-made temperature change (AGW) is true. “Why else, if AGW was not true, would these respectable scientists publish these studies?” people ask themselves. Only, it’s the wrong question.

Each of these studies claim to show a danger that might come to pass given that AGW is true. That is exactly backwards to answering the question of whether AGW is true, however. If instead these studies showed that these maladies already occurred then it might provide some evidence, however weak, to support AGW. But then again, it might also support the theory that the observed climate change is natural and expected. Few or none of these studies show what results to expect given that AGW is false (and climate change natural etc.). To be useful research both scenarios must be analyzed, else we are right to suspect the researcher has been sloppy and perhaps not a little biased toward a specific conclusion.

To be specific: because a study appears showing the harm that AGW might cause it is not, and cannot logically be, proof that AGW is true.

The second problem with these studies is their wearying specificity and confidence, which we alluded to by stating that our zombie researchers “calculated a 32.782412% increase in” attacks. Just joking? At the site Skeptical Science, hosted by an honest man, we find that, given AGW is true, there will be “Increased deaths to heatwaves (5.74% increase to heatwaves compared to 1.59% to cold snaps)”. Really? 5.74% and not 5.73%? Are they sure? Can they even be so confident to say 5.7% and not, for example, 5 or 6%? As a statistician, I can assure you, your model and sample have to be incredibly accurate for you to make verifiable statements to that many decimal places.

These studies almost never give any indication of their uncertainty about their results or assumptions. Instead, the “findings”, or results, are taken to be a given; they are just obviously true. Stating results of a study in this fashion has its intended affect: it increases worry. But it does so to an extent that is almost never warranted. To do risk analysis of a study’s results, accurate estimates of the uncertainty and range of possible effects, including positive ones, must be present, else the study is worthless. Reports without uncertainty and estimates of range of effects again bring up the question of the author’s possible biases.

To be specific again: a research report that does not include measures of uncertainty of its results, and an explicit list of the assumptions and the uncertainty in them, is of almost no use.

The last problem with this research is what you do not see. Again at the site Skeptical Science, the author compiles a list of bad things that will happen if AGW is true, and compares it to a list of good things that will occur. Good things? Yes, of course: because it is impossible that climate change can only be bad. Since about four billion years ago or so, the climate on earth has never been static, nor is it ever expected to be, so to claim, like many do, that any change in climate must be bad is just silly. Responsible scientists of course know this.

But many of them still suspect that any changes will be mostly bad. This is evident scanning the Skeptical Science list. Many items in the “good things” column are unfortunately facetious, for example “Record profits for pharmaceutical companies”, and a “thriving” trade in Mammoth fossils (truly, global warming can cause anything).

There is, naturally, an official psychological name for this sort of behavior, but we don’t need that label to see that if thousands of researchers rush to find the worst that can happen and none (except for corporate “shills”) try and find the best, that there will be an enormous bias in the published literature towards the worst. Add to that the search only for evidence that backs up theories of the worst, and you have the situation we are in now. Which is not quite panic, but extreme distress in some quarters; cries of “Something must be done!” are regularly heard, and any that dare question this necessity are raked over the coals.

It also causes some skeptics of the AGW hypothesis to perhaps lean too far the other way and make statements that they will probably regret later. But these skeptics feel forced to speak out to balance the overly-heated and anxious rhetoric that is generated because these studies get so much press.

To be specific once more: it is irresponsible and harmful not to seek the full range, both good and evil, of what will happen given the climate changes.

My prescription is for restraint among scientists who publish these studies: slow down and do a better job, include estimates of uncertainty, better emphasize limitations, and honestly describe what good might arise whether AGW is true or whether climate change is natural and expected. I predict, however, like the majority of medicinal regimes directed by doctors, that my patients will not be adherent.

Perspective

“The most vehement attack on the wartime press came not from Richard Nixon, but from William Tecumseh Sherman. ‘If I had my choice I would kill every reporter in the world,’ he sighed, ‘but I am sure we would be getting reports from hell before breakfast.’”

Outstanding article (originally linked at the indispensable Arts & Letters Daily) by who else but Victor David Hanson. This article essential reading for all those who expect wars to proceed with Hollywood timing and flawless precision.

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